Development And Application Of A Two-Phase Model For Mixture Of Fluid And Granular Material

Flows of granular-fluid mixture are common and significant phenomena in both nature and industry.To consider the differences in the motion of the fluid and the granular assembly and their interactions,the paper develops a widely applicable two-phase model based on the continuum theory,and explores the mechanisms of gravity-driven granular-fluid mixture flows of different configurations.This paper presents a macroscopic constitutive relationship appropriate for a variety of flow regimes by considering both collisional and frictional mechanisms of granular contacts.Based on the kinetic theory of granular flows,anisotropy collisions between solid particles and the effect of the interstitial fluid on the collisions are taken into account.A formula of frictional stress which can describe the dilatancy of the granular assembly is deduced by combining the yield theory and the statistical relationship between the stresses and the volume change rate of the granular assembly.Employing continuum hypothesis,a two-phase model is developed and the granular and the fluid phases are governed by continuity and momentum equations.The granular pressure and shear stress are calculated by the established constitutive relationship.The interaction forces including drag force,lift force and virtual mass force are formulated.A modified k-e model considering the influence of granular particles is employed to describe the fluid turbulence.The proposed model is firstly validated and applied to dry granular flows.Spatial distributions of granular concentration,velocity,temperature,collisional stress and frictional stress in uniform granular flows are solved.The simulated behaviors of the granular assembly are in good agreement with experimental results for the collapse of granular assembly along slopes with different inclinations.The model is further applied to several classical problems of granular-liquid mixture flows and the complex two-phase interaction mechanisms are explored.In the collapse of underwater granular columns,the fluid dynamic pressure and the interphase drag force are the main causes of the significant differences in collapse characteristics of columns with different initial packing states.For the uniform saturated granular flow along an inclined slope,the spatial distributions of granular concentration,velocity,temperature and diverse forces depend significantly on bottom boundary conditions.Using the VOF method,the model successfully describes the collapse of unsaturated granular columns.The positive effect of high saturation on granular fluidity is accurately captured and the role of the interphase drag force is also analyzed at different stages of the collapse.Finally,the model is applied to simulate the landslide-generated waves at different scales.The model accurately delineates the temporal and the spatial variations of the landslide before and after entering the water,and depicts the generation and the propagation processes of the waves.The effects of the collision and the friction between granular particles and the interphase drag force are identified.The model is utilized to simulate the well-known Lituya Bay event and accurately reproduces the propagation and the run-up processes of the generated waves.